In computational neuroscience, synaptic plasticity rules are often formulated in terms of firing rates. The predominant description of in vivo neuronal activity, however, is the instantaneous rate (or spiking probability). In this article we resolve this discrepancy by showing that fluctuations of the membrane potential carry enough information to permit a precise estimate of the instantaneous rate in balanced networks. As a consequence, we find that rate based plasticity rules are not restricted to neuronal activity that is stable for hundreds of milliseconds to seconds, but can be carried over to situations in which it changes every few milliseconds. We illustrate this, by showing that a voltage-dependent realization of the classical BCM rule achieves input selectivity, even if stimulus duration is reduced to a few milliseconds each.

We investigate the asymptotic version of the Erdős-Ko-Rado theorem for the random kuniform hypergraph H k (n, p). For 2 ≤ k(n) ≤ n/2, let N = n k and D = n−k k . We show that with probability tending to 1 as n → ∞, the largest intersecting subhypergraph of H k (n, p) has size (1 + o(1))p k n N , for any p ≫ n k ln 2 n k D −1 . This lower bound on p is asymptotically best possible for k = Θ(n). For this range of k and p, we are able to show stability as well.A different behavior occurs when k = o(n). In this case, the lower bound on p is almost optimal. Further, for the small interval D −1 ≪ p ≤ (n/k) 1−ε D −1 , the largest intersecting subhypergraph of H k (n, p) has size Θ(ln(pD)N D −1 ), provided that k ≫ √ n ln n. Together with previous work of Balogh, Bohman and Mubayi, these results settle the asymptotic size of the largest intersecting family in H k (n, p), for essentially all values of p and k.

Fast bidirectional replays of place cell activity reflecting previous paths, and stripped off any instantial specifics of the animal's locomotion such as its speed or the duration of stops, have been observed during rest in rodents. Mechanisms underlying replays are not fully understood, as previous models depend on assumptions about the path, and on instantial specifics of motion. Relying on sharp-wave events, dendritic spikes and cholinergic modulation, we propose a spiking network model that stores traversed paths on a behavioral timescale with single exposure and produces fast bidirectional replays of corresponding place cell sequences independent of instantial specifics and the path taken. With the model, we make an experimentally verifiable prediction, the sequence cell population, whose firing follows a predefined sequential activity pattern independent of the environment. Furthermore, we hypothesize a functional role for disinhibition as behavioral time pacemaker, enforcing progression of sequence cell activity to match place sequences traversed.

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Hebbian changes of excitatory synapses are driven by and enhance correlations between pre- and postsynaptic neuronal activations, forming a positive feedback loop that can lead to instability in simulated neural networks. Because Hebbian learning may occur on time scales of seconds to minutes, it is conjectured that some form of fast stabilization of neural firing is necessary to avoid runaway of excitation, but both the theoretical underpinning and the biological implementation for such homeostatic mechanism are to be fully investigated. Supported by analytical and computational arguments, we show that a Hebbian spike-timing-dependent metaplasticity rule, accounts for inherently-stable, quick tuning of the total input weight of a single neuron in the general scenario of asynchronous neural firing characterized by UP and DOWN states of activity.